A series of experiments in deep water conducted in the Large Air-Sea
Interactions Facility (LASIF-Marseille, France) showed that wind
blowing over a short wave group due to the dispersive focusing of
a longer frequency modulated wave train (chirped wave packet) may
increase the time duration of the extreme wave event by delaying
the defocusing stage. These experi-
ments have pointed out that the transfer of momentum and energy
is strongly increased during extreme wave events. Starting from
this fact, a series of nu- merical simulations has been performed
using a pressure distribution over the steep crests given by the
modified Jeffreyssheltering theory. These numerical simulations
corresponding to the dispersive focusing confirms the experimental
results. Furthermore, it was shown numerically that during extreme
wave events the wind-driven current could play a significant role
in their persistence. For more detail see [1]. A similar investigation
has been developed in
finite depth ([2]). Similarly to the deep water case, it was found
that the wind blowing over a strongly modulated wave group due to
the dispersive focusing of an initial long wave packet increases
the duration and maximal amplitude of the steep wave event. In addition,
steep wave events in shallow water are found to be less unstable
to wind perturbation than in deep water. Numerical simulations showed
that the wind speeds up the wave breaking and amplifies slightly
the wave height.

___________________________
Emile Okal, Northwestern Tsunamis as normal modes of the Earth, and a venture into extracurricular
geophysics

In a series of seminal papers, Ward [1980, 1981] has shown that
tsunamis can be interpreted as a special branch of the normal modes
(free oscillations) of a planet including an oceanic layer. This
approach is particularly powerful as it expresses naturally the
coupling between the solid Earth (where most tsunami sources are
located) and the oceanic column, and in particular can handle directly
any intermediate sedimentary structure. Routine algorithms used
in classical seismological synthesis are seamlessly applicable to
tsunami excitation. Normal mode theory is also extended effortlessly
to higher frequencies outside the shallow water approximations,
known to have a crucial effect on the final small scale of harbor
response. On the other hand, its limitations stem from its inability
to handle lateral heterogeneity.

Recently, and especially in the wake of the 2004 Sumatra tsunami,
a number of fascinating observations were made on instruments not
designed for that purpose: in most cases, they express subtle coupling
between media of extremely different properties, such as the oceanic
column, the solid Earth, or the atmosphere. They include recording
of tsunamis by seismometers at land stations and on the ocean bottom,
by hydrophones of the CTBTO, the definitive observation and explanation
of tsunami shadows, tsunami signatures in the geomagnetic field,
the generation of deep infrasound, and the perturbation of the ionosphere
detected on GPS receiver arrays. In most cases, these phenomena
are readily explained by the continuation (in a mathematical sense)
of the tsunami eigenfunction outside of the water column; we will
show that in many instances, the order of magnitude of the effect
is well predicted by simple arguments derived under the normal mode
approach.

This talk is intended to survey our current understanding of tsunamis.
It answers four (or maybe five) basic questions. What is a tsunami?
How do tsunamis work? Does soliton theory apply to tsunamis ? What
can be done to protect people from the dangers of tsunamis? (If
time permits: Why are some some tsunamis deadly and some benign?)

When a solitary wave (a model of tsunami in the nearshore shallow
water) impinges on a reflective vertical wall, it can take the formation
of Mach reflection (a geometrically similar reflection from acoustics).
The mathematical theory predicts that the amplification at the reflection
is not twice, but four times the incident wave amplitude. Evidently,
this has an important implication to engineering design practice.
Our laboratory experiments verify detailed features of the Mach
reflection phenomenon, whereas contradict the theory in terms of
the maximum four-fold amplification: the maximum amplification observed
in the laboratory was 2.92, instead. The reason for the discrepancy
is discussed. In addition, we show that a tsunami along the reflective
wall can reach higher than the maximum solitary wave height. Once
the wave breaking happens along the wall, the substantial increase
in water-surface slope results along the wave crest away from the
wall.